MathDB

3

Part of 2022 Canadian Mathematical Olympiad Qualification

Problems(1)

\sum^{n-1}_{i=0} x_i(3x_i - 4x_{i+1} + x_{i+2}) >= 0

Source: Canada Repêchage 2022/3 CMOQR

10/13/2022
Consider n real numbers x0,x1,...,xn−1x_0, x_1, . . . , x_{n-1} for an integer n≥2n \ge 2. Moreover, suppose that for any integer ii, xi+n=xix_{i+n} = x_i . Prove that ∑i=0n−1xi(3xi−4xi+1+xi+2)≥0.\sum^{n-1}_{i=0} x_i(3x_i - 4x_{i+1} + x_{i+2}) \ge 0.
algebrainequalities